What's the difference between inlet and outlet control?

Inlet control: flow rate is limited by the inlet geometry (orifice flow). Outlet control: friction in the barrel and tailwater determine the headwater. Always compute both — the higher headwater controls.

What's a typical Manning's n for culverts?

Concrete pipe: n = 0.012. Corrugated metal pipe (CMP): n = 0.024. Smooth-lined CMP: n = 0.012. HDPE smooth-bore: n = 0.010. Source: FHWA HDS-5.

When should I use HY-8 instead of this calc?

HY-8 is the FHWA's free culvert design tool. Use it for: complex cross-sections, multi-barrel arrangements, road overtopping analysis, fish-passage criteria, and full performance curves. This calculator is for preliminary sizing within ±10%.

What is HW/D and what value is acceptable?

HW/D is the headwater depth divided by the culvert rise (diameter for circular pipes). Most state DOTs limit HW/D to 1.5 at the design storm and require no road overtopping at the check storm (Q100 or Q500). FHWA recommends HW/D ≤ 1.5 to prevent debris jamming and structural pressures.

How do I calculate culvert outlet velocity?

For inlet control with submerged inlet, outlet velocity ≈ Q / A_full. For outlet control with full barrel, V = Q/A. For partial flow, use Manning's equation at normal depth (typically Q²·n²/(k²·A²·R^(4/3)) = S). Outlet velocities above 10–15 ft/s usually require energy dissipation.

What's the entrance loss coefficient for a square-edged inlet?

K_e = 0.5 for square-edged inlets with headwall. K_e = 0.2 for groove-end inlets. K_e = 0.7 for mitered inlets. K_e = 0.9 for projecting CMP. Lower K_e = better hydraulic performance. Source: FHWA HDS-5 Table 4-1.

Can I use this calculator for box culverts?

This page covers circular culverts only. For box culverts, the inlet-control polynomial uses different coefficients (HDS-5 Table 4-1, Chart 8). Box culverts are commonly square-edged headwall, K_e = 0.5, with full-flow critical depth analysis. Use FHWA HY-8 for box culvert design.

How is tailwater determined?

Compute the normal depth in the receiving channel using Manning's equation at the design discharge. If a downstream control (weir, bridge, confluence) raises the water surface, use HEC-RAS to compute the actual TW. For coastal outfalls, use the maximum of design TW and ocean tide elevation.

All tools Print with PE stamp box Designed for sealed engineering submittals — print drops PE stamp + signature block at the end.

Culvert Hydraulics Calculator

FHWA HDS-5 method. Computes headwater depth for inlet control and outlet control, reports the controlling regime. For circular concrete, corrugated metal, and box culverts.

Units

Culvert type

Diameter, Din

Barrel length, Lft

Barrel slope, S₀m/m or ft/ft

Manning's n— (concrete: 0.012, CMP: 0.024)

Design flow, Qcfs

Tailwater depth, TWft (above outlet invert)

HW (inlet control)—ft

HW (outlet control)—ft

Controlling regime——

Design HW—ft

Defaults: 36-inch concrete pipe, 60 ft long, 1% slope, 40 cfs design flow. SI inputs (mm, m, m³/s) are converted to US internally because the HDS-5 polynomial coefficients are US-customary by definition.

Inlet control (FHWA HDS-5 submerged form, valid for Q/(A·D^0.5) > 4):

$$ \frac{HW_i}{D} = c \left(\frac{Q}{A \, D^{0.5}}\right)^{\!2} + Y - 0.5 \, S_0 $$

Outlet control (energy equation, full-barrel flow):

$$ HW_o = TW + \left(1 + K_e + \frac{29.16 \, n^2 \, L}{R_h^{4/3}}\right) \frac{V^2}{2g} - L \, S_0 $$

HW headwater depth above inlet invert · D barrel diameter · A barrel cross-section area · Q design discharge · c, Y inlet-type coefficients (HDS-5 Table 4-1) · S₀ barrel slope · K_e entrance loss coefficient · n Manning's roughness · L barrel length · R_h hydraulic radius (= D/4 for full circular) · V mean velocity (= Q/A) · TW tailwater depth above outlet invert.

Inlet vs outlet control — read both

A culvert can be controlled by either its entrance geometry (inlet control) or by the friction + velocity head along the entire barrel (outlet control). The actual headwater equals whichever computed value is higher. Steep, smooth culverts are usually inlet-controlled; long, rough, or flat culverts with high tailwater are usually outlet-controlled. The only way to know is to compute both.

Inlet coefficient table (FHWA HDS-5 Table 4-1)

This calculator uses the submerged form (Form 2), accurate when Q/(A·D^0.5) > 4 (typical design-flood condition). The polynomial coefficients c and Y come from Table 4-1 of HDS-5; K_e is the entrance loss coefficient for outlet control.

Submerged inlet-control coefficients for circular culverts (HDS-5 Table 4-1, Chart 1–3)
Inlet type	c	Y	K_e
Concrete pipe, square edge with headwall	0.0398	0.67	0.5
Concrete pipe, groove end with headwall	0.0292	0.74	0.2
Concrete pipe, groove end projecting	0.0317	0.69	0.2
Concrete pipe, beveled edges (33.7° or 45°)	0.0314	0.75	0.2
CMP, headwall (square edge)	0.0379	0.69	0.5
CMP, mitered to conform to slope	0.0463	0.75	0.7
CMP, projecting (no headwall)	0.0553	0.54	0.9
CMP, beveled ring (45°)	0.0300	0.74	0.25

Manning's n for culvert barrels (HDS-5 Table 4-2)
Culvert material / type	n
Concrete pipe, smooth wall	0.012
Concrete box, formed (smooth)	0.013
HDPE, smooth interior	0.010
HDPE, corrugated interior	0.020
CMP, 2⅔ × ½ in. corrugations	0.024
CMP, 3 × 1 in. corrugations	0.027
CMP, 6 × 2 in. corrugations	0.030
CMP with smooth liner (paved invert)	0.018
Spiral rib pipe	0.012
Structural plate, 6 × 2 in. corrugations	0.034

Source: FHWA Publication FHWA-HIF-12-026 (2012). Hydraulic Design of Highway Culverts (HDS-5), 3rd ed.

Worked examples

Example 1 — 36-inch RCP road crossing, Q = 50 cfs

Given: 36-in concrete pipe, groove-end w/ headwall (c = 0.0292, Y = 0.74, K_e = 0.2), L = 60 ft, S₀ = 0.01, n = 0.012, Q = 50 cfs, TW = 2.0 ft.

Find: Controlling HW.

D = 3.0 ft; A = π·9/4 = 7.07 ft²; R = D/4 = 0.75 ft; V = 50/7.07 = 7.07 ft/s

Inlet: Q/(A·√D) = 50/(7.07·1.732) = 4.08; HW_i/D = 0.0292·(4.08)² + 0.74 − 0.5·0.01 = 0.486 + 0.735 = 1.22

HW_i = 1.22 · 3.0 = 3.66 ft

Outlet: 29.16·(0.012)²·60/(0.75)^4/3 = 0.252/0.682 = 0.370

H = (1 + 0.2 + 0.370)·(7.07)²/64.4 = 1.570·0.776 = 1.218 ft

HW_o = max(2.0, 3.0) + 1.218 − 60·0.01 = 3.0 + 1.218 − 0.60 = 3.62 ft

Inlet control governs. HW = 3.66 ft. HW/D = 1.22 ✓

Example 2 — 48-inch CMP, mitered, long flat run, Q = 80 cfs

Given: 48-in CMP, mitered to slope (c = 0.0463, Y = 0.75, K_e = 0.7), L = 200 ft, S₀ = 0.002, n = 0.024, Q = 80 cfs, TW = 3.5 ft.

Find: Controlling HW.

D = 4.0 ft; A = π·16/4 = 12.57 ft²; R = 1.0 ft; V = 6.36 ft/s

Inlet: Q/(A·√D) = 80/(12.57·2.0) = 3.18; HW_i/D = 0.0463·(3.18)² + 0.75 − 0.001 = 0.469 + 0.749 = 1.22

HW_i = 4.87 ft

Outlet: 29.16·(0.024)²·200/(1.0)^4/3 = 3.36; H = (1 + 0.7 + 3.36)·(6.36)²/64.4 = 5.06·0.628 = 3.18 ft

HW_o = max(3.5, 4.0) + 3.18 − 200·0.002 = 4.0 + 3.18 − 0.40 = 6.78 ft

Outlet control governs. HW = 6.78 ft. HW/D = 1.70 ✗ (exceeds 1.5 — upsize, smooth-line, or improve inlet)

When to use each formula

For preliminary culvert sizing on a typical road crossing, this calculator gets you within ±10% of a full FHWA HY-8 analysis at the design flow. For more rigor, you need:

FHWA HY-8 (free download from FHWA website) — full inlet/outlet control with unsubmerged + submerged transitions, performance curves, fish-passage analyses.
HEC-RAS culvert routine — for road overtopping, multi-barrel arrangements, complex tailwater conditions.
Agency-specific design tools — your state DOT may require a specific calculation method for highway crossings.

The simplifications in this calculator: full-flowing barrel for outlet control (assumes Q is enough to fill the pipe — typical at design flood), submerged-form inlet control only, no critical-depth or partial-flow analysis. Document your assumptions when using this for a real submittal.

Common gotchas

Tailwater can dominate. If TW is above the outlet crown, the culvert is operating with a submerged outlet. The energy equation here handles that, but make sure your TW estimate from the receiving channel's normal depth is correct.
Mitered inlets aren't free. Mitering a CMP to match a fill slope looks clean but increases the inlet loss coefficient by 40%+ over a headwall. The hydraulic cost is real.
Multi-barrel culverts split flow. If you have two 36" pipes side-by-side, each carries Q/2 — but the inlet and outlet head losses scale roughly with V², so the per-barrel HW is significantly less than for a single 36" handling Q. Run each barrel separately.

Reference: FHWA Publication FHWA-HIF-12-026 (2012). Hydraulic Design of Highway Culverts (HDS-5), 3rd ed. Polynomial coefficients from Table 4-1.

Related tools

Embed this calculator

Free for course pages, engineering blogs, and reference sites. Copy the snippet:

<iframe src="https://pe-calc.com/embed/culvert.html"
        width="100%" height="600" frameborder="0" loading="lazy"></iframe>

See all available embeds →